TY - JOUR
T1 - On accumulation points of F-pure thresholds on regular local rings
AU - Sato, Kenta
N1 - Funding Information:
The author wishes to express his gratitude to Professor Shunsuke Takagi for his encouragement, valuable advice and suggestions. This work was supported by RIKEN iTHEMS Program.
Publisher Copyright:
© 2023 Elsevier Inc.
PY - 2023/5/15
Y1 - 2023/5/15
N2 - Blickle, Mustaţă and Smith proposed two conjectures on the limits of F-pure thresholds. One conjecture asks whether or not the limit of a sequence of F-pure thresholds of principal ideals on regular local rings of fixed dimension can be written as an F-pure thresshold in lower dimension. Another conjecture predicts that any F-pure threshold of a formal power series can be written as the F-pure threshold of a polynomial. In this paper, we prove that the first conjecture has a counterexample but a weaker statement still holds. We also give a partial affirmative answer to the second conjecture.
AB - Blickle, Mustaţă and Smith proposed two conjectures on the limits of F-pure thresholds. One conjecture asks whether or not the limit of a sequence of F-pure thresholds of principal ideals on regular local rings of fixed dimension can be written as an F-pure thresshold in lower dimension. Another conjecture predicts that any F-pure threshold of a formal power series can be written as the F-pure threshold of a polynomial. In this paper, we prove that the first conjecture has a counterexample but a weaker statement still holds. We also give a partial affirmative answer to the second conjecture.
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U2 - 10.1016/j.jalgebra.2023.02.010
DO - 10.1016/j.jalgebra.2023.02.010
M3 - Article
AN - SCOPUS:85148733822
SN - 0021-8693
VL - 622
SP - 614
EP - 635
JO - Journal of Algebra
JF - Journal of Algebra
ER -